The term "gratuitous promise" may be unique to Scots law, but the concept of a unilateral contract is recognized throughout the Anglo-American jurisprudence

In the United States, the doctrine of “promissory estoppel” overcomes defenses which would ordinarily prevent a gratuitous promise from being considered a binding unilateral contract. Estoppel, in general, is an equitable doctrine under which a party is not allowed to assert a claim or defense because it would be unfair. (Picture the judge stuffing a cork in the opposing party’s mouth.) In the case of promissory estoppel, the party trying to weasel out of an agreement is “estopped” from asserting any of the usual defenses to a contract: no agreement in writing, lack of consideration, that sort of thing.

The theory of promissory estoppel provides:

A promise which the promisor should reasonably expect to induce action or forbearance on the part of the promisee or a third person and which does induce such action or forbearance is binding if injustice can be avoided only by enforcement of the promise.

Restatement (Second) of Contracts § 90(1) (1981)

Note well: the promise has to be something it would be reasonable to expect people to rely on: you can't be legally bound to a promise made jokingly. Context is everything. A textbook case applying promissory estoppel is Drennan v. Star Paving Co., 51 Cal. 2d 409, 333 P.2d 757 (Cal. 1958). A subcontractor submitted an estimate with a bid on a construction project. The general contractor relied on the estimate in setting the price for the general bid. The subcontractor then discovered a mistake in calculating its estimate and tried to revoke it. The court held the estimate could not be revoked. It became binding and irrevocable -- without all the formal requisites for a binding contract-- when the general contractor relied on it, to the general contractor's "detriment" (the general contractor was bound to a bid which would cause a loss if the subcontractor's promise was not enforced).

Other examples include: advertising that a prize or reward will be offered for some action, say, $100,000 if you name your child after the advertiser’s product. If you go ahead and do it, the advertiser must pay the prize, and cannot assert that you failed to get the deal in writing.

Proof of the elements of promissory estoppel also overcomes the defense that a contract must be in writing, the defense which American lawyers refer to as “the Statute of Frauds”, even though the defense is based on common law doctrine, not a statute, on this side of the Atlantic. The term was derived from an English statute “An Act for Prevention of Frauds and Perjuries”, 29 Car. 2, ch. 3, 7 (1677).

The above is offered solely for the reader’s edification and entertainment, not as advice.

I look up citations with Lexis Publishing’s “Law on Disc”.